Probability of Impacting and Accessing Rocks at the MER ... · Probability of Impacting and...

Probability of Impacting and Accessing Rocks at the MER

Landing Sites

M. P. Golombek, A. Haldemann, E. DiMaggio, R. Schroeder, and J. Matijevic

4th MER Landing Site WorkshopJanuary 8-10, 2003

Embassy Suites, Arcadia

1/7/2003 M. Golombek2

Probability of Impacting or Accessing Rocks

• Use Model Size-Frequency Rock Distributions and Thermal Differencing Rock Abundance Estimates to Determine Frequency of Potentially Hazardous & Measurable Rocks

• Not for the Faint of Heart; Lots of Uncertainties– Assumes IR Rock Abundance is Accurate (~20-25%) from Scale of

IR Pixel to Landed Surface [THEMIS]– Assumes Rock Abundance is Made up of Individual Rocks– Outcrops and Non-Uniform Distributions– Assumes Model Rock Distributions are Representative and Apply

• But [Best Can Do with What Have Now]

– IRTM Rock Abundances are 3 for 3, within 20% of Landed Count– Rock Distribution Models Appear Representative of Many Natural

Surfaces - On Earth and Mars: Fracture & Fragmentation Theory– Model Accurately Predicted Distribution of Rocks at MPF Site


Viking Lander Rock Distributions

0.0001

0.001

0.01

0.1

0.01 0.1 1

Rock Diameter (m)

VL1 Far Field - Crater Rim

VL1 Crater Rim (2000 m2)

VL1 Far Field (20000 m2)

VL1 Near Field

VL2

Power Law

Cumulative Area versus Diameter -

Exponential Decay

Cumulative Area is RockAbundance

VL1 w/o Outcrops


Rock Distributions on Earth

0.001

0.01

0.1

1

0.01 0.1 1

Rock Diameter (m)

VL2VL1

AvawatzGDB2

MH:TOTMH:NE/SE/SW

MH:NENESEGDT3

GDB1NGDB1S

EF TotalEF7

EF4EF3

Cumulative Area versus Diameter -

Same Exponential

Wide Variety SurfacesWeathered VolcanicEphrata FanAlluvial Fan

Fracture & FragmentationTheory - Failure By Propagation of Ubiquitous Flaws


Rock Distributions in Hawaii

0.0001

0.001

0.01

0.1

1

Diameter (m)

MR1

MS4

MS3

MS2

MS1

EKDF

KD1

MU1

HP1

POP2

POP1

PE5

PE4

PE3

PE2

PE1

Same Exponential Shape

Wide Variety of Surfaces: Fresh & Weathered Lava Flow Surfaces, Chemically Weathered, Frost Shattering, Phreatic Eruptions, etc.

w/R. Craddock & A. Howard


Model Rock Size-Frequency Distributions

0.001

0.010

0.100

1.000

0.01 0.1 1

Diameter (m)

0.02 0.05 0.2

0.3

VL 1

VL 2

0.1

Fk(D) = k exp [-q(k) D]

Fk(D) Cum. Frac. Area

k is Total Rock Abundance

q(k) Governs Drop with D

q(k) = 1.79 + 0.152/k

Predicted 0.01 Area at MPF

Covered by Rocks D>1 m


Prediction Successful!

Measured Rocks inMPF Near and Far FieldMatch Model for MPF IRTM RockAbundance

0.0001

0.001

0.01

0.1

0.1 1 10

VL1VL2MPF

Cum

ulat

ive

Fra

ctio

nal A

rea

Diameter (m)


Boulders in MOC Images

Counted Bouldersin MOC Images as Check on Large Dia. Rock Distribution

Boulders Show Up asLight/Dark Pixel Pairsin Low Sun Images

480 m Dia. Crater; Largest Boulder 14 m250 Boulders Counted1 pixel Rock=1.5 m Dia

M0201741


Boulder Fields in MOC Images

MOC Image (M0402248) Olympus Mons Caldera Scarp Boulder Field, 45° Sun Angle, 6 m/pixel 5182 Boulders, Max 24 m

M0202582 Graben Floor 39° Sun Angle, 3 m/pixel

4143 Boulders, Max Rock 12 m Diameter

Rockiest Locations on Mars


Boulder Size-Frequency Distributions

• Boulder Fields Rare– ~0.1% of MOC Image– Low Sun >38°

• Plotted Max Subareas– Ave, Min 2-10 x Lower

• Extreme Distributions– Steep Slope, Exponential

Decay– Similar to Model Dist.

• ~1% Surface Covered by 3-10 m Diameter Boulders

• Can’t See Boulders at 3 Landing Sites, 20%– If Can’t See, <20% Rock

Abundance

0.0001

0.001

0.01

0.1

0.1 1 10

VL1VL2MPFCrater RimOly MonsGraben FloorGraben FloorGusev S2Gusev Q2

Cum

ulat

ive

Fra

ctio

nal A

rea

Diameter (m)


Boulders at Mars Pathfinder Site

Highest Resolution (1.5 m/pixel ) MOC Image of MPF Landing Site

Boulders Difficult to Identify, Even though MPF Among Rockiest Locations on Mars, ~20%

If Can’t See Rocks in MOC Images then No Rockier than MPF, ~20% Rock Abundance

Largest Rocks Visible from Lander Difficult to See in Highest Resolution MOC Images


Cumulative Number Inversion

Numerically Integrate CumulativeArea Curves

Predict Cumulative Number of Rocks/m2 of Diameter D or Greater for Any Rock Abundance

In General, H=D/2So 1 m Dia Rocks are 0.5 m High

MPF ~0.01 Rocks/m2 D>1 mMPF Bounced 15-20 TimesEach Bounce ~15 m2

MPF 200-300% Chance Hit D>1 mor 100% Chance Hit 2-3 D>1 mRocks without Damage

Cum# Rocks in MPF Far Field Consistent with the Lack of Boulders >3 m Dia in MOC Images

10-6

10-5

0.0001

0.001

0.01

0.1

1

10

0.1 1 10

VL1VL2MPFCrater RimOly MonsGraben FloorGraben FloorGusev S2Gusev Q2

Cum

ulat

ive

Num

ber

of R

ocks

/m2

Diameter (m)


Airbag Drop Test Platform

60° Dipping Platform at Plum BrookLargest Vacuum Chamber in World

Fully Inflated AirbagsAround Full ScaleLander

Bungee Chord PullsLander to ImpactVelocities

Airbags Impact Firstat Edge BetweenTetrahedrons &Then Rotates to Face


MER Airbag Drop Tests

Mostly Sharp Andesites, All Rocks Chalked, Placed at Key Locations to Test Lobe Edges and Bladder


Airbag Drop Tests

Airbags Have BeenTested to ExtremeCumulative Numberversus DiameterDistributions: 20 to >40%

Tests 5-10Times Greater Number of 1 m Diameter Boulders than at MPF or VL20.01

0.1

1

10

0.1 1

VL1VL2MPFMPF BMER 3C/DMER 36MER 37MER 60/45MER 01MER 04MER 2-3AMER 02

Cum

ulat

ive

Num

ber

Roc

ks/m

2

Diameter (m)


Airbag Drop TestsAirbags Have Been Tested ToExtreme Cum.Area versusDia. Distributions:20->40% Model

10% SurfaceCovered by 1 mDiameter Rocks

30% SurfaceCovered by>0.4 m Diameter Rocks

0.01

0.1

0.1 1

VL1VL2MPF5% Model10% Model20% Model30% Model40% ModelMPF BMPF AMER 3C/DMER 36MER 37MER 60/45MER 01MER 04MER 2-3AMER 02

Cum

ulat

ive

Fra

ctio

nal A

rea

Diameter (m)


Shape and Burial of Rocks

• Triangular Rocks >0.2 m High– Failure Due to Stress Exceeding Tensile Strength Interior Bladder– Angular Rocks More Likely to Tear/Abrade Outer Layers– Added Second Interior Bladder (No Failures Since)

• Burial of Rocks Important– Deeply Buried Rocks Don’t Move During Impact– More Likely to Stress Interior Bladder– More Likely to Abrade Outer Layers

• Assessed Shape of Rocks at 3 Landing Sites/Drop Platforms• Used Burial Data [Deeply, Partially Buried, Perched]


ROCK SHAPE

Round• Hemispherical, very weathered

or smooth (“stimpy”)

Square• Large flat surfaces, nearly

horizontal surfaces, distinct edges (“flat top”)

Triangular• Distinctly angular rock, pyramid

shaped (“mini matterhorn”)

Triangular Rocks Most Hazardous; Round Least Hazardous3 Independent Observers, 2/3 Majority


Shape of Rocks in Airbag Test Platforms

Number of RocksH (m) Tri Sq Rnd0.5 4 80.4 2 100.3 29 51 140.2 2 5 1Tot 31 62 33

H (m) is rock height in mTri are triangular shaped rocksSq are square shaped rocksRnd are round shaped rocks

25% of Rocks on PlatformTriangular and Deeply Buried


Landing Site Rock Burial & ShapeNumber of Rocks

Perched Partially Buried BuriedLand H (m) Tri Sq Rnd Tri Sq Rnd Tri Sq RndSite

VL1 0.2 10.1 8 2 6 10 2 10 1 1 3

VL2 0.5 10.4 1 1 10.3 1 1 1 20.2 3 3 1 4 2 3 3

MPF >0.5 1 20.4 10.3 1 10.2 1 2 3 20.1 3 2 8 6 12 16


Landing Sites Compared with Test Platform Rocks

• Rocks at 3 Landing Sites Higher than 0.2 m– 1/3 Rocks are Triangular– 14% Rocks are Deeply Buried– 19% Rocks are Triangular and Deeply or Partially Buried– 7% Rocks are Triangular and Deeply Buried

• Airbag Test Platform Rocks– 25% are Triangular– All are Deeply Buried (aka Firmly Attached)

• Airbag Test Platform Rocks More Hazardous (~3 Times) than Rocks at 3 Landing Sites


Probability Encountering Rock

• Assume Cum. # Rocks Modeled by Poisson Distribution– Suggested by Distribution of Rocks Measured at Landing Sites– Appropriate for Distributions Produced by Natural Processes

• L, number of rocks per unit area - assumed to be uniform• Probability, p, of a single rock in any given area, c, is

– proportional to c, as p = 1/(c L)

• Probability of exactly n rocks in any area (c L) – P(n, c L) = (c L)n exp(-c L)/n!

• The probability that at least one rock of a specified size is within the area c is given by the equation– 1 - P(0, c L) = 1- exp(-c L)


Probability of Impacting Rock at Landing Sites

• Chose Diameter D>1 m; Roughly 0.5 m High– D>0.4 m, 1/3 Triangular, – 7% Triangular & Deeply Buried

• Take IRTM Rock Abundance [Christensen, 1986]– Pixels Cover Significant Portion of Ellipse

• Cumulative Number Rocks from Model Inversion• Airbag Bounce Areas - 16.98 m2 or 8.95 m2

– Rolling Bounce (Horizontal Velocity) or Flat Face

• Calculate Probability for 2, 4, 10, 60 Bounces– First 2 Most Energetic– Next 2 Possibly Energetic (spinup)– After first 10 Bounces Less Energetic; 60 Bounces Max.


Model Cumulative Number Rocks

10-6

10-5

0.0001

0.001

0.01

0.1

1

10

0.1 1 10

VL1

VL2

MPF

5% Model

10% Model

20% Model

30% Model

40% Model

Cum

ulat

ive

Num

ber o

f Roc

ks/m

2

Diameter (m)

Model Yields Cumulative Number of

Rocks/m2 of Diameter D or

Greater for IRTM Rock

Abundance at Landing Sites


Landing Site IRTM Rock Abundance

• TM20B, Hematite: Average 5% – (pixels 1, 6, 6, 7%)

• EP55A, Gusev: Average 7.5% – (pixels 7, 8% plus a small bit of 3%)

• IP84A, Isidis: Average 14% – (pixels 13, 15%)

• EP78B2, Average 5% or 6.3% – (7 pixels are 1, 6, 6, 6, 8, 6% plus a small bit of 11%)


Probability (%) of Impacting a Rock >1 m Dia.

96.0-99.8

41.5-63.9

19.3-33.5

10.2-18.4

0.00615-16

VL1, VL2, MPF, Isidis(max)

93.2-99.4

36.1-57.2

16.4-28.8

8.6-15.6

0.00513Isidis (min)Melas (max)

65.8-87

16.4-28.8

6.9-12.7

3.5-6.6

0.0028Gusev,Elysium (max)

41.5-63.9

8.6-15.6

3.5-6.6

1.8-3.3

0.0017Meridiani(max)Gusev (ave)

19.3-33.5

3.5-6.6

1.4-2.7

0.7-1.3

0.00045Meridiani,Elysium (ave)

0.54-1.01

0.09-0.17

0.04-0.07

0.02-0.03

0.000012Meridiani,Elysium (min)

Prob (%)60

Bounces

Prob (%)10

Bounces

Prob (%)4

Bounces

Prob (%)2

Bounces

Cum. # Rocks/m2>1 mDia.

IRTM RockAbun(%)

LandingSite


Risk From >1 m Diameter Rocks• Airbags Have Been Tested Successfully Against 1 m Diameter

(0.5 m High) Rocks, Multiples/Bounce• Engineering Analysis Likelihood Failure Does Not Increase Until

Height>0.7 m (1.5 m Dia.)– For Higher Rocks Risk Rises Slowly with Lander Velocity & Orientation

• Rapid Drop Off in Model # with Increasing Diameter• 10 Times Fewer 1.5 m Diameter Rocks (vs 1 m)

– <0.14%, <0.27%, & <0.68% in in 2, 4 & 10 bounces for 8% Rock Abundance: Max. at Meridiani, Elysium, Ave. Gusev

• 100 Times Fewer 2 m Diameter Rocks (vs 1 m)– <0.03%, <0.07% and <0.17% in 2, 4, and 10 bounces: 8% Rock

Abundance: Max. at Meridiani, Elysium, Ave. Gusev

• Gusev Boulder Fields-Cum# Rocks 0.00014 and 0.0006/m2>4 m– Prob. Impact 1.1-2.0%, 2.1-4.0%, 5.2-9.7% 2, 4, 10, and 60 bounces– Larger Rocks probably not hazardous, surface curvature ~ width

tetrahedral airbag face-react as if impacting a planar surface.


Probability (%) of Impacting a Rock >0.4 m Dia.

37.6-59.2

89.4-98.6

99.9-100.0

0.215-17

VL1, VL2, MPF, Isidis (max)

16.1-28.4

56.8-79.6

91.9-99.2

0.068Gusev (ave),Elysium (max)

3.7-6.9

16.4-28.8

41.5-63.9

0.035Meridiani,Elysium (ave)

0.9-1.6

4.1-7.6

11.8-21.2

0.0072Meridiani,Elysium (min)

Prob (%)2 BouncesTriangular/

Buried Rocks

Prob (%)2 BouncesTriangular

Rocks

Prob (%)2 BouncesAll Rocks

Cum. # Rocks/m2>0.4 m Dia.

IRTM RockAbun(%)

LandingSite

Prob. rock >0.4 m Dia. Actually Hazardous is Less-Bladder failure likely controlled geometry of airbag/rock; Second airbag bladder may have eliminated this failure mode


Proximity of Rocks to MER for Study

• Rocks >0.1 m Dia. Large Enough to be Measured• Rocks >0.3 m Dia. Large Enough to be RAT-ed

– without moving

• Cum.# rocks/m2 > 0.1 m and 0.3 m Dia. – From model for IRTM rock abundance at landing sites

• 2 Areas Evaluated– 0.9 m Annulus (~18.5 m2) Images beyond Solar Array

Obscuration, Easy Single Sol Drive – Area (3.14 m2) IDD Placed in one command cycle, 2 m from

front of vehicle-within Hazcam stereo coverage


MER Access Areas

High GainAntenna(HGA)

Pancam Calibration

Target

Low GainAntenna(LGA)

Navcam (pair)

Pancam (pair)

Pancam MastAssembly PMA)

InstrumentDeploymentDevice (IDD)

FrontHazcam

(pair)

Rocker-BogieMobility System

In-situ Instruments (APXS, MB, MI, RAT)

WarmElectronicsBox (WEB)

SolarArrays

RoverEquipment

Deck (RED)

UHFAntenna

Capture/Filter Magnets


Expected Proximity of Rocks

99.96.067.70.361009.4315-17

VL1, VL2, MPF, Isidis(max)

95.72.841.40.1799.65.61.88Gusev,Elysium(max

791.423.20.08496.83.41.15Meridiani,Elysium(ave)

34.80.3870.02394.12.80.92Meridiani,Elysium(min)

Probability (%) of at least One Rock> 0.3 mDia. In Area

within ~3 Rover Lengths

Expected Number of Rocks> 0.3 m Dia. In

Area within ~3 Rover Lengths

Probability (%) of at least One

Rock> 0.3 mDia. In IDD

Area

Cum. # Rocks/m2>0.3 m Dia.

Probability (%) of at least One Rock> 0.1 m Dia. In IDD Area

Expected Number of

Rocks> 0.1 m Dia.

In IDD Area

Cum. # Rocks/m2>0.1 mDia.

IRTM RockAbun(%)

LandingSite

At All Sites-Rocks Large Enough to be Analyzed in IDD Workspace PlentifulAt All Sites-Rocks Large Enough to RAT within Easy 1 Sol Drive


Conclusions

• Model Rock Distributions-Exponential Fit to Viking Predicted MPF– Used to Calculate Probability Rocks in Impact, Workspace & Drive Areas

• Rock Distributions in Airbag Tests Extreme– Similar to 50-60% Model Rock Distributions– Rock Shape and Burial 3 Times Worse than at 3 Landing Sites

• Probability of impacting a >1 m Diameter Rock– ~1%, ~2%, & ~5% in 2, 4, or 10 bounces for Meridiani & Elysium average

5% rock abundance & ~5-6 times higher at Gusev; 10 times higher at Isidis

• Probability of impacting >1.5 m diameter – <<1% in 10 bounces at Meridiani, Elysium and Gusev

• Probability of impacting a buried triangular rock >0.2 m high– <2% in 2 bounces at Meridiani, Elysium and Gusev (assuming fraction of

buried triangular rocks similar to the three landing sites)

• Rocks large enough to be measured & abraded should be plentiful – within the IDD workspace & within an easy single Sol’s drive by the rover

Date post:	09-Nov-2018
Category:	Documents
Upload:	hoangdieu
View:	213 times
Download:	0 times

Probability of Impacting and Accessing Rocks at the MER ... · Probability of Impacting and...

Documents